The Scalar Field in Extreme Reissner–nordström–de Sitter Space

Abstract

By generalizing the method of I. Brevik et al. the scalar field equation between the outer black hole horizon and the cosmological horizon in the extreme Reissner-Nordström-de Sitter (RNdS) geometry is solved. The field amplitude, as well as the potential, is shown graphically by introducing the "tangent " approximation, which is more exact than that used by I. Brevik et al., of the tortoise coordinate. There are two limiting cases of our special interest. The first one is when the cosmological horizon is very close to the outer horizon of the "black hole." The second one is when they are far apart. And the reflection and transmission coefficients are worked out in the two cases respectively.

The Real Scalar Field Equation for Nariai Black Hole in the 5d Schwarzschild–de Sitter Black String Space

“…Here, scalar particles are only considered. Recently, Higuchi et al [5] and Grispino et al [6] gave the scalar field solution outside a Schwarzschild black hole; Brady et al [7], Brevik et al [8] and Tian et al [9] studied the Schwarzschild-de Sitter (SdS) case; Guo et al [10] made further studies in the Reissner-Nordström-de Sitter one. As for recent studies of searching evaporating black holes, one can refer to the works [11] [12] [13].…”

“…Its robust non-zero magnitude engages the researching interest in the space contained cosmological constant. Especially, the black hole contained effective cosmological constant is studied widely either in higher dimensions background [26] [27] [24] or in usual 4D case [7] [8] [9] [10]. Sometimes for the sake of study, Λ is considered as a free parameter like in the works [8] [9] [10].…”

“…Especially, the black hole contained effective cosmological constant is studied widely either in higher dimensions background [26] [27] [24] or in usual 4D case [7] [8] [9] [10]. Sometimes for the sake of study, Λ is considered as a free parameter like in the works [8] [9] [10]. In SdS space, the interval between black hole horizon r e and cosmological horizon r c becomes smaller with increase value of Λ.…”

Real Scalar Field Scattering with Polynomial Approximation around Schwarzschild-de Sitter Black-hole

“…[3] Many researchers have developed various methods and techniques to study the black-hole by using the radiating particles, such as the simple Klein-Gordon particles and Dirac particles (for some early works, see Damour and Ruffini [4] and Chandrasekhar [5] respectively). Recently, as for scalar field, Higuchi et al [6] and Grispino et al [7] gave its solution outside a Schwarzschild black-hole, Brady et al [8] studied the Schwarzschild-de Sitter case and Guo et al [9] made further studies in the Reissner-Nordström-de Sitter one.…”

The real solution to scalar field equation in 5D black string space

“…Since then, many people have used various methods and techniques to research black hole through the particles radiating from it, such as the simple Klein-Gordon particles and Dirac particles (for some early works, see Damour and Ruffini [3] and Chandrasekhar [4] respectively). Recently, as for the former scalar field, Higuchi et al [5] and Grispino et al [6] gave the scalar field solution outside a Schwarzschild black hole, Brady et al [7], Brevik et al [8] and Tian et al [9] studied the Schwarzschild-de Sitter case and Guo et al [10] made further studies in the Reissner-Nordström-de Sitter case and so on.…”